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,XACT  MEASUREMENTS 


IN 


EDUCATION 


JAMES  LEROY  STOCKTON,  A.  M.  (Columbia) 

SUPERINTlfeNDENT    ELEMENTARY    DEPARTMENT 
NdE>IAL   SCHOOL,  WINONA,  MINN. 


CHICAGO  NEW  YORK 

ROW,  PETERSON  &  COMPANY 


Digitized  by  the  Internet  Archive 

in  2007  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/exactnneasurementOOstocrich 


EXACT  MEASUREMENTS 

IN 

EDUCATION 


JAMES  LEROY  STOCKTON,  A.  M.  (Columbia) 

SUPERINTENDENT  ELEMENTARY  DEPARTMENT 
NORMAL  SCHOOL,  WINONA,  MINN. 


CHICAGO  NEW  YORK 

ROW,  PETERSON  &  COMPANY 


o 


^■d 


Copyright,  1915 

BY 

James  LeRoy  Stockton 


Vv>^  ^ 


v^ 


EXACT  MEASUREMENTS 

IN 

EDUCATION 

THESES 

I.  Measurement  in  Education  should  have  for 
its  goal  the  computation  of  work  and  rate-of-work 
(power),  in  the  sense  in  which  these  terms  are 
used  in  Mechanics. 

II.  Scales  of  force,  space,  and  time,  exist,  or 
can  be  made,  for  school  subjects;  and  the  stand- 
ard units  of  these  scales  of  force,  and  space,  and 
time,  should  be  combined  into  standard  units  of 
work  and  rate-of-work  (power),  such  units 
directly  corresponding  to  the  foot-pound  and  the 
horse-power.  (In  this  paper  units  are  worked 
out  for  penmanship,  and  illustrated  by  experi- 
mental work  involving  certain  applications  of  the 
Thorndike  Scale.) 

III.  Many  units  in  many  school  subjects  should 

331230 


4  EX4CJT  MEASTJKEMENTS 

be  supplemented  by  a  single  unit,  making  possible 
the  computation  of  mental  work  and  rate-of- 
mental-work  (mental  power)  in  all  school  sub- 
jects. The  force  involved  in  this  computation  is 
intelligence;  the  space  is  measured  in  elements  of 
expression.  (As  there  is  no  adequate  scale  of 
intelligence  uncombined  with  any  mechanical  fac- 
tor, a  theory  of  the  necessary  scale  is  ventured.) 

IV.  In  any  case,  to  consider  either  force,  space, 
or  time,  alone,  or  to  combine  them  in  an  arbitrary 
manner,  gives  unreliable  results.  [This  is  shown, 
for  computations  in  school  subjects,  by  the  pen- 
manship illustration.  For  computations  of  men- 
tal work,  and  mental  power,  experience  with  the 
Binet-Simon  tests  is  cited  in  proof  of  the  con- 
tention.] 


EXACT  MEASUEEMENTS  IN  EDUCATION 

I 

Most  persons  do  not  any  longer  question  the 
possibility  of  measurement  in  Education,  because 
it  has  become  apparent  that  measurements  always 
have  been  made,  and  are  continuing  to  be  made. 
When  it  is  said  that  a  piece  of  work  is  good,  bad, 
or  indifferent,  a  measuring  scale  of  at  least  three 
steps  is  evidently  being  used.  If  papers  are 
marked  A,  B,  C,  D,  E,  according  to  the  judgment 
of  the  examiner,  a  scale  of  five  steps  is  being  used. 
This  is  clearly  evident;  measurement  is  a  fact 
in  all  departments  of  Education  whenever  the 
value  of  the  product  is  expressed. 

There  are,  however,  many  conscientious  think- 
ers who  still  question  the  degree  of  exactness  to 
which  the  measurement  should  be  carried.  The 
common  rough  measurements  which  are  con- 
stantly used  do  not  seem  so  objectionable  as  the 
more  exact  scientific  measurements  which  are 
being  proposed.  It  is  feared  that  too  much  exact- 
ness will  make  Education  formal  or  mechanical. 


6  EXACT  MEASUREMENTS 

If  this  fear  were  justifiable  it  would  furnish  a 
very  strong  foundation  for  a  stand  against  meas- 
urement, for  modern  Education  cannot  defend 
formalism.  Fortunately,  however,  the  difficulty 
can  be  met  with  the  following  statements : 

(1)  Education,  in  so  far  as  it  can  be  measured, 
is  a  product, 

(2)  Mechanical  methods  of  measuring  a  prod- 
uct do  not  require  mechanical  methods  of  pro- 
ducing that  product.  Handwriting  might  be 
measured  by  the  most  mechanical  means  one  could 
imagine,  and  yet  have  been  produced  by  the  freest, 
most  spontaneous  method  that  exists.  The  worst 
that  can  be  said  is  that  mechanical  measurement 
may,  in  the  careless  and  unthoughtful,  tend  to 
produce  mechanical  methods  of  production;  but 
pre-supposing  reasonable  thoughtfulness  in  its 
use,  nothing  promises  more  for  Education  than 
does  exact  scientific  measurement. 

In  this  work  progress  has  been  made  through 
the  establishment  of  relatively  exact  scales  in 
certain  school  subjects ;  but  the  progress  has  been 
slow,  as  it  always  is  in  a  new  field.  Confusion, 
also,  is  beginning  to  result,  because  the  plunge 
into  this  undiscovered  country  has  naturally  been 


IN  EUUCAXroN  7 

made  with  no  very  definite  route  marked  out  in 
advance,  and  with  no  very  adequate  conception 
of  the  extent  of  the  territory  to  be  explored. 
There  is  not  much  evidence  that  it  is  realized  that 
the  making  of  scales  may  be  merely  a  scouting 
on  the  frontier  —  merely  the  beginnings  of  roads 
whose  end  lies  in  a  more  remote  country.  If 
this  should  prove  to  be  true  much  wandering  will 
be  prevented  if  a  return  is  made  to  the  starting 
point,  and  an  attempt  made,  in  the  light  of  all 
past  experience,  to  map  the  whole  route  from 
the  beginning  to  the  end.  Then  if  the  map  shows 
districts  to  be  traversed  in  which  as  yet  no  road 
exists,  the  problem  will  at  least  be  clear  when 
these  sections  are  reached. 

It  is  the  purpose  of  this  paper  to  suggest  that 
an  unexplored  district  does  exist  in  the  field  of 
measurement  in  Education,  and  that  the  making 
of  scales  takes  the  investigator  only  part  way  on 
the  road  to  the  final  goal.  An  attempt  will  be 
made  to  show  that  even  with  the  scales  now  avail- 
able, or  with  other  similar  ones  which  may  be 
made,  still  another  step  must  be  taken  or  Educa- 
tion remains  in  the  same  condition  as  was  the 
science  of  Mechanics  before  the  time  of  Watt. 


8  EXACT  MEASUREMENTS 

Before  Watt  the  scales  of  feet,  pounds,  and  min- 
utes were  in  use,  but  there  was  no  attempt  to  use 
them  in  a  computation  of  work  and  rate-of-work 
by  means  of  the  composite  units  called  the  foot- 
pound and  the  horse-power.  The  formulation  of 
these  units  opened  a  new  realm  in  Mechanics. 
From  now  on  this  discussion  will  deal  with  the 
hypothesis  that  there  is  such  a  new  realm  in 
measurement  in  Education,  and  that  all  of  our 
efforts  in  this  field,  including  the  making  of  scales, 
will  gain  in  definiteness  and  worth  through  being 
directed  toward  this  final  goal  —  the  computation 
of  work  and  rate-of-work;  work  being  used  in  its 
technical  meaning  for  the  science  of  Mechanics. 

Any  hypothesis,  in  order  to  justify  itself,  must 
show  wherein  it  meets  conditions  unmet  before; 
it  gains  its  adherents  through  its  ability  to  clear 
up  existing  confusions,  and  to  present  worthy 
results.  Therefore  the  problem  squarely  in  view 
is  (1)  to  show  that  there  is  confusion,  (2)  to  show 
that  this  hypothesis  clears  up  at  least  some  of  it, 
and  (3)  to  show  that  the  results  from  the  applica- 
tion of  the  hypothesis  are  reasonable  and  valuable. 

There  are  at  least  three  points  where  confusion 
exists.     The  first  is  clearly  stated  by  Whipple, 


IN  EDUCATION  9 

^*  Manual  of  Mental  and  Physical  Tests/'  as  fol- 
lows. ^'  The  question  arises:  shall  efficiency  be 
measured  in  terms  of  quality,  excellence,  delicacy, 
or  accuracy  of  work,  or  shall  it  be  measured  in 
terms  of  quantity,  rate,  or  speed  of  work?  For 
this  question  no  general  answer  can  be  given." 
Certain  expedients  are  then  suggested,  but  no 
final  and  exact  program  is  outlined.  An  attempt 
will  be  made  to  show  that  the  hypothesis  of  work 
clears  up  the  problem  of  the  true  relation  between 
quantitative  and  qualitative  scales,  which  is  the 
real  problem  propounded  in  the  foregoing  quota- 
tion. Another  source  of  confusion,  distinct,  but 
indirectly  included  by  Whipple  in  the  lines  just 
quoted,  lies  in  the  treatment  of  the  time  element 
involved  in  testing.  This,  when  considered  at  all, 
is  ordinarily  carried  as  a  separate  index;  but  in 
many  cases  there  is  a  tendency  to  neglect  it 
entirely,  often  with  grave  results,  as  happens 
when  two  schools  are  compared  in  handwriting, 
without  any  consideration  of  the  time  involved 
in  the  production  of  the  specimens.  The  need 
for  a  separate  index  vanislies  under  the  hypothe- 
sis of  worJc,  and  time  receives  its  legitimate  and 
necessary  emphasis.    The  third  source  of  confu- 


10  EXACT  MEASUREMENTS 

sion  is  in  the  conception  of  efficiency  itself.  This 
conception  is  vague  and  indefinite.  Various  defi- 
nitions are  contending  for  recognition.  All  school 
measurement  is  supposed  to  be  directed  toward 
the  determination  of  relative  efficiency,  and  yet 
there  is  disagreement  as  to  what  constitutes  true 
efficiency.  There  can  be  no  such  disagreement 
under  the  hypothesis  of  work. 

These  claims  for  the  hypothesis  must  now  be 
more  closely  examined  and  tested.  This  task  will 
be  furthered  by  an  analysis  of  mechanical  work 
and  rate-of-work.  As  already  indicated,  before 
the  time  of  Watt  the  scales  of  feet,  of  pounds,  and 
of  minutes,  were  in  use.  It  was  therefore  possible 
to  know  that  a  force  of  5047.00  pounds  was  at 
work  where  it  was  found  necessary  to  exert 
another  force  of  5047.00  pounds  against  it  —  as 
in  lifting  against  the  force  of  gravity.  It  was 
also  easily  seen  that  another  valuable  formulation 
could  be  made  if  distance  were  included.  To  say 
that  one  machine  lifted  a  weight  of  5047.00  pounds, 
and  another  a  weight  of  5556.00  pounds,  led 
naturally  to  the  idea  that  the  second  machine  was 
the  stronger;  but  as  soon  as  the  distance  was 
taken  into  consideration  a  doubt  was  raised.    If 


IX  EDUCATION"  H 

the  first  machine  raised  5047.00  pounds  four  feet, 
and  the  second  machine  raised  its  5556.00  pounds 
four  feet  or  more  the  doubt  as  to  the  greater 
strength  of  the  second  madhine  did  not  exist. 
But  if  the  first  machine  raised  5047.00  pounds 
four  feet  and  the  second  machine  raised  5556.00 
pounds  tJiJ^ee  feet,  indefiniteness  as  to  strength 
was  apparent.  It  was  possible  to  carry  the  two 
indexes  in  each  case  (5047.00  pounds  lifted  four 
feet,  and  5556.00  pounds  lifted  three  feet)  and  to 
get  certain  rather  valuable  results.  One  could 
say  that  he  preferred  the  smaller  amount  lifted 
the  greater  distance,  or  the  larger  amount  lifted 
the  smaller  distance;  but  the  computation  of  work 
from  these  data  made  a  single  index  possible,  put 
definiteness  into  exact  comparison  of  the  two,  and 
so  opened  the  new  realm  as  previously  mentioned. 
Quoting  from  a  modern  text  in  physics: 
*^  "When  a  body  acted  upon  by  a  force  moves  in 
the  direction  in  which  the  force  is  acting,  work  is 
said  to  be  done.  *  ^  *  The  amount  of  work 
done  is  measured  by  the  product  of  the  force  by 
the  distance  which  the  body  moves  along  the  line 
of  the  action  of  the  force.  Thus  when  a  two 
pound  weight  is  raised  three  feet,  it  moves  a  dis- 


12  EXACT  MEASUREMENTS 

tance  of  three  feet  against  a  force  of  two  pounds 
and  therefore  six  foot-pounds  of  work  is  done 
against  the  force  of  attraction  of  the  earth."* 

Work,  therefore,  in  Mechanics  means  force 
acting  through  space,  and  is  computed  by  the 
formula  W  =  F  X  S.  Where  work  is  to  be  con- 
sidered, force  alone  means  nothing  and  space 
alone  means  nothing;  but  force  acting  through 
space  means  ivorh,  and  a  certain  unit  of  force 
(the  pound)  acting  through  a  certain  unit  of 
space  (the  foot)  means  a  certain  unit  of  work 
(the  foot-pound).  This  unit  of  work  may  be 
briefly  expressed  as  unit  force  acting  through 
unit  space.  By  means  of  this  unit  the  two  ma- 
chines above  referred  to  may  be  definitely  com- 
pared as  to  the  work  they  do.  One  machine  did 
work  equal  to  5047.00X4.00,  or  20188.00  foot- 
pounds. The  other  did  work  equal  to  5556.00  X 
3.00,  or  16668.00  foot-pounds.  The  relative  work- 
ing ability  of  the  two  machines  is  definitely  ex- 
pressed by  the  ratio  of  20188.00  to  16668.00. 

But  there  is  still  another  element  to  be  con- 
sidered; viz.,  that  of  time.    The  amount  of  work 


•Kimball  —  '*  College  Physics." 


IN  EDUCATION  13 

is  the  same  whether  5047.00  pounds  be  lifted  4.00 
feet  in  one  minute  or  in  one  hour  or  in  one  year; 
but  it  is  often  important  to  know  for  various  rea- 
sons, at  what  rate  this  work  can  be  delivered. 
Hence  another  unit  (a  certain  amount  of  work 
delivered  in  a  certain  time)  becomes  necessary. 
If  a  definite  amount  of  work  in  a  definite  time  is 
taken,  it  is  not  important  just  what  the  amount 
or  the  time  may  be,  except  for  considerations  of 
convenience.  But  if  there  is  no  unit  agreed  upon, 
two  indexes  must  be  carried  as  before,  and  com- 
parisons are  again  cumbersome.  20188.00  foot- 
pounds in  five  seconds,  must  perhaps  be  compared 
with  16668.00  foot-pounds  in  51/2  seconds.  In 
order  to  do  this  it  must  all  be  put  upon  the  basis 
of  amount  delivered  in  one  second  by  dividing 
the  number  of  foot-pounds  of  work  by  the  time. 
20188.00  foot-pounds  divided  by  5.00  =  4037.60 
foot-pounds    per    second;    16668.00    foot-pounds 

divided  by  5.50  =  3030.54  foot-pounds  per  second. 

« 

These  can  now  be  compared  with  each  other. 

But  it  is  still  better  to  have  a  standard  unit  of 
accomplishment  per  second  and  compare  all  other 
accomplishments  with  the  unit.  Watt  selected  as 
the  unit  of  rate-of-work  the  number  of  foot- 


14  EXACT  MEASUREMENTS 

pounds  per  second  accomplished  by  the  average 
horse  (550.00  foot-pounds  per  second).  He  could 
have  used  any  other  number,  but  this  number 
proved  convenient.  Using  it  as  a  unit,  it  is  seen 
that  the  machine  which  did  4037.00  foot-pounds 
per  second  was  a  7.34  horse-power  machine.  The 
machine  which  did  3030.55  foot-pounds  per  second 
was  a  5.51  horse-power  machine.  These  two 
results  admit  of  immediate  and  perfect  compari- 
son, and  the  formulation  of  this  method  of  com- 
puting rate-of-work  (or  power,  as  the  physicist 
calls  it)  opened  to  Mechanics  the  second  part  of 
the  new  realm,  as  the  computation  of  work  itself 
opened  the  first  part  of  that  realm. 

In  attempting  to  appropriate  for  Education 
this  new  field  of  work  and  rate-of-work  (power) 
it  is  necessary  to  formulate  units  of  work  and 
rate-of-work  (power)  based  upon  either  an  anal- 
ogy to,  or  an  identity  with,  force  acting  through 
space  in  time.  Examination  of  the  situation 
seems  to  show  a  real  identity.  That  which  is 
measured  in  Education  is  always  some  kind  of 
expression  through  movement  occurring  in  space, 
which  movement  is  controlled  (changed)  either  in 
direction  or  magnitude  by  some  agent.    The  dif- 


IN  EDUCATION  15 

ferences  which  we  measure  in  handwriting  are 
differences  in  direction  and  magnitude  of  motion, 
registered  on  paper  in  the  form  of  letters.  Even 
thought  itself  becomes  manifest  and  can  be  meas- 
ured only  in  terms  of  expression,  which  expres- 
sion is  in  movement,  resolved  in  the  last  analysis 
into  changes  in  direction  or  magnitude.  Now  the 
only  name  the  world  has  ever  had  for  that  which 
changes  the  motion  of  a  body,  either  in  direction 
or  amount,  is  force.  There  seems  to  be  no  reason 
for  calling  the  agent  behind  expression  by  any 
other  name  than  force.  It  meets  the  definition  of 
force,  and  is  measured  as  all  force  must  be ;  i.,  e. 
in  terms  of  its  products.  There  is  therefore  an 
identity  between  one  element  in  units  of  work 
and  rate-of-work  (power)  in  Mechanics,  and  the 
same  element  in  Education.  (This  affirmation  of 
identity  is  meant  to  carry  only  so  far  as  the 
assertion  that  the  agent  behind  achievement  in 
Education  is  a  force.  This  force  may  differ  from 
other  forces,  just  as  electrical  force  probably 
differs  from  gravitational  force  etc.) 

But  all  of  the  movements  which  are  initiated 
and  controlled  by  the  force,  take  place  in  space 
^r4  time.     That  is,  the  force  acts  through  the 


16  EXACT  MEASUREMENTS 

space  in  the  production  of  the  given  movement  in 
the  given  time.  In  handwriting  when  a  word  is 
written,  the  force  (or  control)  acts  through  the 
space  roughly  measured  by  the  linear  arrange- 
ment of  letters,  this  measurement  being  exactly 
parallel  to  the  rough  measurement  of  space  by 
paces  or  other  such  linear  units,  used  before  the 
more  accurate  foot  and  inch  where  selected  as 
units.  The  addition  of  the  time  element  here  as 
elsewhere,  provides  for  the  computation  of  rate- 
of-work,  or  power.  This  relation  between  force, 
space,  and  time  is  not  an  arbitrary  but  a  natural 
and  necessary  relation.  Physics  demonstrated 
and  adopted  it;  physics  did  not  create  it.  The 
relation  between  the  factors  is  a  universal  rela- 
tion which  is  found  wherever  the  three  factors 
are  involved. 

Hence  it  seems  inevitable  to  apply  this  prin- 
ciple in  Education  in  a  manner  similar  to  its  use 
in  Mechanics.* 


♦Reference  is  made  earlier  in  this  paper  (page  . . )  to 
certain  attempts  (see  Whipple,  Manual  of  Mental  and 
Physical  Tests)  to  correlate  these  factors.  Reference 
should  also  be  made  to  Brown's  excellent  article  on 
Reading  in  the  Elementary  School  Teacher  for  June, 


IN  EDUCATION  17 

An  attempt  will  now  be  made  fully  to  illustrate 
and  to  apply  the  idea  in  the  field  of  handwriting, 
since  it  is  there  that  the  most  suitable  scales  nec- 
essary to  the  formation  of  the  units  are  found. 
In  handwriting  there  is  motion  under  varying 
degrees  of  control.  This  control  which  alters  the 
direction  and  magnitude  of  motion  is  a  force. 
But  the  force  here  presents  a  complication  of  two 
factors;  viz.,  conscious  direction,  which  may  be 
called  intelligent  force,  or  intelligence ;  and  habit, 
which  is  mechanical.  It  follows  that  the  motion, 
then,  is  a  resultant  of  the  action  of  more  than 
one  force;  but  this  does  not  alter  anything  in 
relation  to  the  computations.  A  resultant  of  two 
or  more  forces  is  dealt  with  under  the  same  laws 
as  are  simple  forces.  The  one  thing  which  must 
be  remembered  in  this  connection  is  that  because 
the  force,  intelligence,  is  combined  with  a  mechan- 
ical factor,  the  work  computed  cannot  be  called 
purely  mental  work  but  mere  penmanship  work. 


1914,  and  to  others.  In  all  cases,  however,  which  have 
come  under  the  observation  of  the  writer  of  this  article, 
arbitrary  relations  have  been  established  among  the  fac- 
tors, and  the  necessary  and  permanent  relation  has  been 
disregarded. 


18  EXACT  MEASUREMENTS 

In  the  second  part  of  this  paper  the  discussion 
of  the  computation  of  purely  mental  work,  where 
the  force  involved  is  intelligence  alone,  is  con- 
sidered. 

Now  in  order  to  make  the  formulation  of  units 
possible,  there  must  be  a  scale  of  the  force  and  a 
scale  of  the  space.  Then  the  standard  unit  of  the 
scale  of  force  can  be  combined  with  the  standard 
unit  of  the  scale  of  space  into  the  standard  unit  of 
penmanship  work ;  and  the  standard  unit  of  pen- 
manship work,  complicated  with  the  standard  unit 
of  a  scale  of  time,  can  be  the  standard  unit  of  rate- 
of -penmanship  work,  or  penmanship  power.  But 
can  the  force  involved  in  penmanship  work  be 
measured?  Not  directly,  any  more  than  the  force 
of  gravity  can  be  measured  directly.  But  the 
force  of  gravity  is  measured  by  its  effects  (ten- 
sion of  a  spring),  and  the  force  involved  in  pen- 
manship work  can  be  measured  by  one  of  its 
effects;  viz.,  the  amount  of  quality  exhibited  by 
the  handwriting  produced.  This  amount  of 
quality  is,  roughly  at  least,  measured  by  the 
Thorndike  handwriting  scale,  and  the  idea  of 
such  a  scale  is  apparently  sound  and  capable  of 
refinement.    Of  this  more  will  be  said  later.    In 


IN  EDUCATION  19 

the  meantime  this  scale  will  be  used  as  a  means 
of  continuing  the  illustration ;  and  it  should  con- 
tinue to  be  used  for  purposes  of  school  measure- 
ment until  a  better  one  takes  its  place,  or  until 
it  is  further  made  more  nearly  perfect. 

Let  unit  force  (or  control)  be  that  control 
which  produces  penmanship  which  exhibits  the 
amount  of  quality  designated  as  No.  1  of  the 
Thorndike  scale^^  Let  unit  space  be  the  space 
measured  by  one  letter.  Then  if  a  person  writes 
60.00  letters  equal  to  No.  12.00  quality  Thorndike 
scale,  the  work  involved  is  force  X  space  or  60.00 
X  12.00  or  720.00  units  of  work.  These  units 
correspond  to  foot-pounds  and  should  be  desig- 
nated by  some  name  of  similar  significance. 

It  is  necessary  at  this  point  to  guard  against 
the  idea  that  the  plan  as  outlined  above 
identifies  force  with  quality  of  handwriting,  and 
space  with  quantity  of  handwriting.  The  quality 
of  the  writing  is  not  the  force,  but  it  is  the 
measure  of  the  force;  the  number  of  letters  is 
not  the  space,  but  it  is  the  measure  of  the  space. 

Since  quantity  and  quality  are  here  mentioned, 
it  seems  best  to  discuss  them  further  in  order  to 
show  that  the  plan  does  give  the  combination  of 


20  EXACT  MEASUREMENTS 

quantitative  and  qualitative  scales  which  solves 
the  vexed  question  (as  claimed  earlier  in  the 
paper).  When  it  is  said  that  a  person  does  60.00 
letters  of  No.  12.00  quality  in  a  minute,  and  work 
is  computed  by  finding  the  product  of  60.00  and 
12.00  according  to  the  formula  W  =  F  X  S, 
viewed  superficially  it  seems  as  if  force  were 
identified  with  quality  and  space  with  quantity, 
and  that  the  two  (quantity  and  quality)  were 
merely  multiplied  together  as  a  solution  of  the 
quantity-quality  difficulty.  But  force  is  not  iden- 
tified with  quality  nor  space  with  quantity;  and 
when  60.00  is  multiplied  by  12.00  force  is  not 
being  multiplied  by  space  (as  the  formula  F  X  S 
would  seem  to  imply)  but  a  measure  of  force  is 
multiplied  by  a  measure  of  space,  as  previously 
indicated.  Neither  when  60.00  is  multiplied  by 
12.00  is  quality  multiplied  by  quantity;  but  a 
quantity  of  quality,  used  as  a  measure  of  force, 
is  multiplied  by  another  quantity  of  quality,  used 
as  a  measure  of  space.  The  Thorndike  scale  is 
a  quantity-quality  scale.  No.  1  handwriting  as 
measured  by  the  scale  exhibits  a  certain  amount 
(quantity)  of  handwriting  quality;  No.  12.00 
handwriting,   following   the  assumption   of   the 


IN  EDUCATION  21 

author  of  the  scale,  exhibits  an  amount  of  hand- 
writing quality  12.00  times  as  great  as  that 
exhibited  by  No.  1  handwriting.  That  is  to  say 
that  what  we  designate  as  No.  12.00  quality  is  not 
quality  alone,  but  quantity  of  quality.  It  is  the 
same  with  space.  The  unit  of  space  in  writing 
is  the  letter.  This  is  rough,  as  has  been  admit- 
ted, but  letters  arranged  in  linear  fashion  meas- 
ure the  space  much  as  it  might  be  measured  by 
more  or  less  irregular  paces.  60.00  paces  means 
60.00  movements  of  pace  quality.  Spaces  and 
paces  have  many  qualities  all  of  which  are  not 
held  in  common,  but  one  quality  is  common 
to  both;  viz.,  extension.  Hence  the  extension 
involved  in  paces  is  often  used  to  measure  the 
extension  of  space.  In  like  manner  it  is  pro- 
posed to  use  the  quality  of  extension  involved  in 
letters  as  a  measure  of  the  extension  of  space. 
One  letter,  therefore,  is  equal  to  a  unitary 
amount  (quantity)  of  the  space  quality  known 
as  extension.  Therefore  the  multiplication  of 
60.00  by  12.00  in  the  problem  above  cited,  and  in 
all  similar  problems,  while  it  seems  to  be  a  mul- 
tiplication of  quantity  by  quality,  and  actually 
settles  our  confusion  as  to  the  relation  of  these 


22  EXACT  MEASUREMENTS 

scales,  is  really  a  multiplication  of  a  quantity  of 
quality  by  another  quantity  of  quality,  or  in  other 
words  a  multiplication  of  quantity  by  quantity. 
A  summary  of  points  thus  far  made  follows : 
Exact  measurement  in  Education  is  desirable 
and  much  has  been  done;  but  there  is  a  realm 
into  which  it  has  not  been  extended ;  this  is  the 
realm  of  work.  Computation  of  work  requires 
the  consideration  of  force  acting  through  space. 
There  must  be  a  quantitative  scale  of  some  meas- 
ure of  the  force,  made  in  definite  standard  units 
which  can  be  counted,  and  the  steps  of  the  scale 
must  bear  a  definite  and  known  relation  to  one 
another.  There  must  also  be  a  definite  scale  of 
the  space,  meeting  the  same  conditions  as  does 
the  scale  for  the  measurement  of  the  force.  Then 
the  standard  units  of  these  scales  must  be  com- 
bined into  a  composite  unit  of  work,  comparable 
to  the  foot-pound.  So  far  it  has  been  shown  how 
the  conditions  can  be  met  for  handwriting:  the 
Thorndike  scale  is  used  as  the  measure  of  the 
force.  No.  1  handwriting  being  the  unit;  letters 
are  used  to  measure  the  space,  one  letter  being 
the  unit.  Combining  these  standard  units  into 
a  composite  unit  of  work  gives  One  Letter  — 


IN  EDUCATION  '  23 

No.  1.00  T  scale  as  the  result;  the  60.00  letters 
No.  12.00  T  scale  equal  720.00  units  of  work 
(using  the  formula  W  =  F  X  S). 

Now  it  becomes  necessary  to  compute  rate-of- 
work,  and  a  unit  must  be  found.  When  Watt 
wished  to  compute  rate-of-work  (power)  he  had 
to  settle  upon  a  representative  number  of  foot- 
pounds per  unit  of  time  as  a  unit.  So  for  hand- 
writing there  must  be  selected  a  certain  number 
of  letters  No.  1.00  T  scale  per  unit  of  time.  Any 
number  would  do,  provided  that  it  was  definite 
and  agreed  upon,  and  used  by  every  one.  But 
for  comparative  purposes  (in  order  that  the  unit 
may  stand  as  a  sort  of  goal  of  achievement)  it 
is  desirable  that  the  number  be  put  at  some  point 
near,  probably  slightly  above,  the  average  combi- 
nation of  speed  and  control  possible  for  the 
average  seventh  and  eighth  grade  public  school 
pupil.  However,  since  all  seventh  and  eighth 
grade  public  school  pupils  write  above  No.  1.00 
T  scale  handwriting,  it  is  most  feasible  to  get 
the  average  of  both  speed  and  control  for  such 
pupils,  and  then  to  reduce  that  number  to  No. 
1.00  quality. 

If  these  suggestions  are  carried  out  and  the 


24  EXACT  MEASUREMENTS 

right  computations  made,  there  is  added  to  meas- 
urement in  handwriting  (and  by  the  same  meth- 
ods there  could  be  added  to  the  measurement  of 
any  other  school  subject)  the  realm  of  computa- 
tion of  'work  and  rate-of-work  (power)  which 
Watt  added  to  Mechanics.  The  tendency  in 
handwriting  measurement  has  been  to  take  the 
product  of  one  school  and  measure  by  the  Thorn- 
dike  (or  other)  scale  and  get  the  average  control. 
Then  to  take  another  school  and  do  the  same  and 
compare  the  two  results.  This  is  exactly  similar 
to  that  measurement  in  Mechanics  which  con- 
siders how  much  a  machine  can  lift  against  the 
force  of  gravity  but  does  not  ask  through  what 
space  the  force  acts,  nor  in  what  time  the  effort 
is  performed.  Some  investigators  have  seen  this 
difficulty  and  have  set  a  time  limit  upon  the 
making  of  the  specimens  and  have  counted  the 
words  or  letters  written  in  a  certain  time.  But 
these  results  have  been  carried  in  a  form  not 
suitable  for  actual  comparisons.  It  is  much  as 
if  one  tried  to  compare  two  machines  by  saying 
the  one  could  lift  ten  pounds  two  feet  in  one 
second,  and  the  other  nine  pounds  two  and  one- 
half  feet  in  one  second,  without  trying  to  com- 


IN  EDUCATION  25 

pute  the  work  or  the  rate-of-work  (power;  in- 
volved. To  make  units  of  work  and  rate-of-work 
(power)  for  penmanship  (or  other  school  sub- 
jects) solves  the  time  problem  mentioned  in  the 
early  part  of  this  paper,  as  it  has  been  shown 
to  have  solved  the  quantity-quality  problem. 

But  in  order  to  put  the  plan  fully  into  opera- 
tion for  handwriting,  there  is  needed  a  knowl- 
edge of  how  many  letters,  and  what  quality  of 
letters,  the  average  seventh  and  eighth  grade 
public  school  pupil  writes  per  minute.  To  get 
at  least  preliminary  light  upon  this  matter,  fifty 
such  pupils  were  tested.  Copying  from  the 
printed  page  under  a  set  time  limit  was  at  first 
tried.  Each  pupil  wrote  three  tests  representing 
(1)  his  ordinary  work,  (2)  his  fastest  work,  and 
(3)  his  best  work.  These  papers  wore  scored 
for  control  by  the  Thorndike  handwriting  scale, 
and  for  space  by  the  counting  of  the  number  of 
letters  on  the  paper.  Next  an  attempt  was  made 
to  get  truer  data  for  writing  per  se,  by  eliminat- 
ing the  perception  element  so  common  in  the 
copying.  This  was  done  by  asking  the  children 
to  write  memorized  material.  There  were  three 
five  minute  tests  as  before;  viz.,   (1)   ordinary, 


26  EXACT  MEASUREMENTS 

(2)  rapid,  (3)  best.  The  tests  were  given  to  the 
children  collectively  and  the  papers  scored  as 
before  for  control  and  space.  In  all  of  the  tests 
the  same  instructions  were  given  to  all  of  the 
children,  the  same  part  of  the  day  was  used,  and 
in  general,  the  usual  precautions  were  taken  to 
insure  uniform  validity  in  the  results. 

Below  is  a  table  giving  averages  and  the  devia- 
tions from  the  average  for  both  control  and  space 
in  the  full  series  of  six  tests. 
Abbreviations  used: 

0.  C. — Ordinary  Copying    0.  M. — Ordinary  Memory 
H.  C. — Hurried  Copying      H.  M. — Hurried  Memory 
B.  C. — Best  Copying  B.  M.— Best  Memory    . 

Av.  =  average;  the  tables  are  per  minute  of  time. 

SPACE 


Av. 


Av. 


o.c. 

H.C.    B.C. 

O.M. 

H.M. 

B.M. 

54.02 

77.48    49.60 

CO'TEOL 

75.07 

94.10 

60.07 

O.C. 

H.C.    B.C. 

O.M. 

H.M. 

B.M. 

11.16 

10.44    11.40 

10.48 

9.66 

10.90 

IN  EDUCATION  27 

AvEEAGB  Deviations  (from  average) 


Av. 


Av. 


SPACE 

o.c. 

H.C.    B.C. 

CM. 

H.M. 

B.M. 

12.56 

9.57      8.20 

CONTEOL 

9.79 

12.30 

9.48 

O.C. 

H.C.    B.C. 

CM. 

H.M. 

B.M. 

.83 

1.10        .84 

1.20 

1.40 

.82 

This  table  does  not  involve  enough  cases  to 
prove  anything;  but,  in  addition  to  presenting 
other  interesting  information,  it  does  throw  light 
upon  the  question  as  to  what  constitutes  a  reason- 
able unit  of  rate-of-work  (power)  in  penmanship. 
No  medians  are  given,  but  they  correspond  very 
closely  to  the  various  averages,  and  there  seems 
to  be  little  choice  as  to  whether  conclusions  shall 
be  drawn  from  the  one  or  from  the  other.  Since 
the  results  are  suggestive  only,  it  is  simpler  to 
deal  with  the  averages  only.  The  table  of  devia- 
tions will  show  that  the  deviation  from  the  aver- 
age is  but  eight  to  twelve  letters  (or  about  two 
ordinary  words)  per  minute. 

While  fast  handwriting  and  best  handwriting 
present  much  material  for  comparison,  it  is,  after 


28  .  EXACT  MEASUREMENTS 

all,  rather  certain  that  ordinary  writing  is  the 
best  general  measure.  More  than  this,  the 
tests  marked  **  ordinary  memory  "  are  naturally 
selected,  for  '*  ordinary  copying  "  was  interfered 
with  by  the  perception  element.  It  will  be  seen 
that  the  space  units  under  ordinary  memory  are 
75.07  and  the  control  units  10.48.  The  work  is 
75.07  X  10.48  (F  X  S)  or  786.73.  Approximately 
this  result  has  been  selected  as  a  possible  unit  of 
rate-of-work  (780.00  letters  of  unit  control  in  one 
minute).  Certain  undiscussed  aspects  of  the 
problem  make  it  seem  that  the  factors  here 
involved  would  represent  a  better  standard  to 
strive  for  if  the  relation  were  changed  to  65.00 
and  12.00.  This  combination  represents  the  same 
number  of  units  of  work  (780.00)  and  will  be 
dealt  with  in  this  paper  tentatively  as  the  stand- 
ard. Thorndike  in  his  monograph  on  hand- 
writing suggests  the  same  amount  of  work  (60.00 
letters  of  13.00  times  unit  control)  as  a  limit 
beyond  which  it  is  useless  to  train  children  in 
this  subject. 

The  tentative  units  ^suggested  for  handwriting 
are  therefore: 


IN  EDUCATION  29 

Unit  of  work  =  One  Letter  — No.  1.00  T  scale. 
Unit  of  rate-of-work  (power)  =  780.00  letters 
—  No.  1.00  T  scale,  in  one  minute. 

If  this  represents  a  fair  achievement  in  hand- 
writing, or  if  it  does  not  and  yet  can  be  agreed 
upon  as  a  measure,  it  will  furnish  a  much  more 
accurate  and  fair  means  of  comparison  than  has 
heretofore  been  in  use. 

The  handwriting  of  pupil  No.  1  scaled  12.00 
(Thorndike  scale).  The  handwriting  of  pupil 
No.  5  scaled  10.00.  Using  the  Thorndike  scale 
as  it  is  often  used,  this  is  as  far  as  the  matter 
would  be  carried  and  it  would  be  said  that  pupil 
No.  1  was  the  better  pupil  in  handwriting.  What 
can  rightly  be  said  is  that  pupil  No.  1  exhibited 
the  most  handwriting  control.  But  it  is  impor- 
tant also  (for  complete  comparison)  to  deal  with 
other  factors.  First,  through  what  space  was 
this  average  control  sustained?  Through  265.00 
letters  for  pupil  No.  1,  and  through  387.00  letters 
for  pupil  No.  5.  Now  which  is  *^  better  "  — 
265.00  letters  of  No.  12.00  control  or  387.00  letters 
of  No.  10.00  control?    There  has  been  no  way  of 


30  EXACT  MEASUREMENTS 

telling  at  all  accurately,  and  no  system  of  eom- 
putation  will  ever  tell  which  is  better.  The  ques- 
tion of  best  all  depends  upon  the  definition  of 
best,  upon  the  aim  toward  which  the  work  is 
directed,  and  upon  the  degree  to  which  the  aim  is 
accomplished.  For  certain  purposes,  387.00  let- 
ters of  No.  10.00  control  may  be  much  better  than 
265.00  letters  of  No.  12.00  control  (or  vice  versa). 
Control  may  for  certain  purposes  be  preferred 
to  space,  or  excessively  slow  writing,  for  certain 
other  purposes,  may  not  be  so  good  as  more 
rapid  work  of  less  control.  But  though  the 
knowledge  of  the  aim  may  change  the  judgment 
as  to  which  is  best,  it  does  not  at  all  change  the 
amount  of  work  delivered.  This  amount  of  work 
delivered  is  a  constant  (for  pupil  No.  1,  265.00  X 
12.00  units  of  work)  and  to  make  use  of  it  opeiis 
to  Education  one-half  of  the  new  realm  of  work 
added  to  Mechanics  by  Watt. 

Pupil  No.  1  did  265.00  letters  of  No.  12.00 
control,  or  3180.00  units  of  work.  (A  name  must 
be  coined  for  this  unit.) 

Pupil  No.  5  did  317.00  letters  of  No.  10.00  con- 
trol, or  3170.00  units  of  work. 

To  have  tried  to  compare  these  two  items  by 


IN  EDUCATION  31 

carrying  the  two  indexes  would  have  been  indefi- 
nite and  burdensome;  but  to  compare  3180.00 
with  3170.00  is  simple  and  accurate.  [This 
means  accurate  to  the  degree  to  which  the  scales 
involved  are  accurate,  and  though  the  scales  are 
rough  as  yet,  they  are  capable  of  refinement.  A 
partial  discussion  of  this  matter  follows  later  in 
regard  to  the  Thorndike  scale.] 

It  is  desirable  also  to  add  the  time  element  and 
to  know  which  of  these  pupils  worked  at  the 
faster  rate,  for  time  is  always  an  important 
factor  in  any  task,  although  there  are,  of  course, 
occasions  when  one  is  willing  to  sacrifice  this 
element  to  other  elements.  Pupil  No.  1  did 
3180.00  units  of  work  in  5.00  minutes,  or  636.00 
units  per  minute.  Since  780.00  units  per  minute 
has  been  tentatively  selected  as  a  standard  unit 
of  rate-of-work,  this  pupil  No.  1  exhibited  less 
than  one  standard  unit  of  rate-of-work  (power); 
i.  e.  636.00  divided  by  780.00  =  .81  units  of  rate- 
of-work  (power).  A  name  must  also  be  coined 
for  this  unit.  This  name  will  correspond  to  the 
^^horse-power''  as  used  in  Mechanics,  as  the 
name  for  the  penmanship  unit  of  work  will  corre- 
spond to  the  foot-pound.    Pupil  No.  2  did  3170.00 


32  EXACT  MEASUREMENTS 

units  of  work  in  5.00  minutes,  or  634.00  units  per 
minute.  634.00  divided  by  780.00  =  .81  units  of 
rate-of-work  (power). 

Here  are  two  pupils  who  in  work  delivered 
(computed  to  two  decimal  places)  are  equal;  but 
no  such  judgment  could  have  been  made  from  a 
mere  examination  of  the  data,  or  from  the  carry- 
ing of  separate  indexes.  A  definite  unit  of  rate- 
of-work  (power)  based  upon  a  unit  of  work 
makes  this  comparison  possible. 

Even  at  the  risk  of  being  called  to  account  for 
unnecessary  repetition,  it  must  again  be  said 
that  there  is  no  thought  that  these  computations 
have  proved  what  is  the  best  condition.  They 
have  merely  expressed  accurately  the  facts  of  the 
condition.  The  question  of  best  or  worst  is  to 
be  decided  on  the  basis  of  the  aims  for  the  work. 
One  may  go  intelligently  about  the  task  (on  the 
basis  of  his  aim)  of  producing  any  ratio  between 
the  factors  of  force-time-space  that  he  may  desire. 
Any  adjustment  of  these  factors  may  be  sought, 
just  as  in  the  movement  of  physical  weights  a 
small  force  working  through  a  long  distance  may 
be  preferred,  or  a  large  force  working  through 
a  short  distance.    The  time  element  may  also  be 


IN  EDUCATION  33 

long  or  short  —  all  of  these  elements  varying 
according  to  the  aim. 

However,  should  there  still  be  a  desire  to 
retain  in  these  combination  results,  the  evidence 
by  means  of  which  at  any  time  the  exact  figures 
for  control  and  space  could  be  regained,  it  may 
be  done  by  the  following  process,  and  at  the  same 
time  a  valuable  element  may  be  added  to  the 
final  result.  Pupil  No.  1  was  found  to  be  worth 
.81  units  of  rate-of-work  (power),  because  he 
wrote  265.00  letters  of  No.  12.00  times  unit  con- 
trol in  5.00  minutes,  or  53.00  letters  of  No.  12.00 
times  unit  control  in  one  minute.  His  space  was 
therefore  53/65  of  normal  and  his  control  12/12 
of  normal.  These  fractions  may  be  observed, 
and  on  the  basis  of  the  aim  for  this  work  (which 
may  require  a  preponderance  of  space  or  con- 
trol) judgment  may  be  made  as  to  whether  or  not 
the  combination  is  a  good  one.  To  facilitate  this 
judgment  the  answer  may  be  written  .81,  (53/65 
X  12/12).  But  this  notation  will  be  all  the  more 
valuable  if  these  fractions  are  reduced  to  deci- 
mals, since  their  relation  will  then  be  much 
plainer.  Following  out  this  suggestion  for  the 
students  just  compared,  it  is  written  that 


34  EXACT  MEASUREMENT 

pupil  No.  1  delivered  .81  units,  (.81  X  1.00) ; 
pupil  No.  5  delivered  .81  units,  (.97  X  0.83). 

The  same  method  of  comparison  may  be  used  for 
two  schools.  Below  is  a  table  giving  averages 
and  deviations  from  the  average,  in  space  and  in 
control,  for  fifty  normal  school  girls,  in  six  tests 
similar  to  those  reported  upon  for  grade  chil- 
dren. Following  the  table  is  a  comparison  of 
certain  records  of  the  normal  school  girls,  with 
corresponding  records  of  the  grade  children. 
Abbreviations  used: 


O.C. -^Ordinary  Copying    0.  M.— Ordinary  Memory 
H.  C— Hurried  Copying     H.  M. — Hurried  Memory 
B.  C. — Best  Copying  B.  M. — Best  Memory 

Av.  ==  average ;  the  tables  are  per  minute  of  time. 


Av 


Av. 


SPACE 

o.c. 

H.C.  B.C. 

CM.  H.M. 

B.M. 

r....  74.88 

99.66  73.56 

CONTEOL 

91.96  111.00 

81.74 

0.  c. 

H.C.  B.C. 

CM.  H.M. 

B.M. 

r....   11.50 

11.00  11.80 

11.56  10.30 

11.78 

IN  ErUCATION  35 

Average  Deviations  (from  average) 


Av. 


Av. 


SPACE 

o.c. 

H.C.    B.C. 

O.M. 

H.M. 

B.M. 

11.52 

12.46      9.42 

CONTBOL 

9.84 

12.18 

10.75 

O.C. 

H.C.    B.C. 

O.M. 

H.M. 

B.M. 

.66 

.68        .56 

.67 

1.07 

.69 

To  compare  the  records  in  ordinary  copying 
the  following  computations  are  made: 

Normal  girls  space  average  74.88 ;  control  aver- 
age 11.50.  74.88  X  11.50  =  861.12 ;  861.12  divided 
by  780.00  =  1.10,  (74.88/65.00  X  11.50/12.00)  or 
1.10,  (1.15  X. 95). 

Elementary  school  space  average  54.02;  con- 
trol average  11.16.  54.02  X  11.16  =  602.86; 
602.86  divided  by  780.00  =  .77,  (54.02/65.00  X 
11.16/12.00,  or  .77,  (.83  X  .93). 

By  merely  looking  at  the  tables  it  could  be 
seen  that  at  all  points  in  both  space  and  control, 
the  normal  school  students  were  ahead  of  those 
in  the  elementary  school.  It  would  also  be  pos- 
sible to  tell  how  much  they  were  ahead  in  space 
and  in  control,  each  one  being  considered  sepa- 


36  EXACT  MEASUREMENTS 

rately ;  but  without  some  such  process  as  the  one 
suggested  it  could  never  be  told  how  much  the 
normal  school  was  ahead  in  the  actual  amount 
of  work  delivered.  But  having  computed  the 
amount  delivered  in  each  case,  the  comparison 
could  be  made. 

It  is  known  also  that  more  work  was  done  than 
was  delivered.  There  was  loss,  just  as  there  is 
loss  in  the  working  of  an  engine  where  fric- 
tion and  other  causes  subtract  from  the  power 
actually  delivered.  No  machine  delivers  as  much 
work  as  it  actually  does,  and  the  percentage 
delivered  varies  constantly  from  day  to  day  and 
even  from  hour  to  hour  or  moment  to  moment. 
To  say  that  a  machine  is  ten  horse-power,  means 
that  it  averages  ten  horse-power,  or  that  it  is 
ten  horse-power  at  the  time  that  the  measure- 
ment is  made,  A  badly  adjusted  carburetor  or 
an  excess  of  friction  at  a  given  point  may  make 
a  gas  engine  lose  almost  any  per  cent  of  its 
power,  even  to  not  being  able  to  run  at  all.  A 
horse  grown  nervous  from  misuse  may  ^*  jump 
up  and  down  "  in  one  place  and  pull  nothing. 
A  child  (metaphorically  speaking)  might  do  the 
same  thing  when  nervous  over  being  asked  to 


IN  EDUCATION  37 

do  his  best  work,  or  when  indifferent  through 
lack  of  motive  (as  might  be  true  of  ordinary 
work).  He  does  a  large  amount  of  work,  per- 
haps, or  possibly  he  does  not.  Theoretically  he 
should  put  into  his  work  his  whole  self  and  the 
same  se]f  each  time,  and  deliver,  without  waste, 
an  equal  amount  of  work  in  a  given  time,  even 
though  the  factors  of  force,  space,  and  time 
varied  in  the  different  cases.  Practically  he  does 
not  put  in  each  time  his  whole  self  or  the  same 
self,  and,  also,  there  are  many  other  sources  of 
loss,  so  that  in  given  periods  of  five  minutes,  or 
other  time  space,  the  amount  of  work  actually 
delivered  varies.  Data  computed  from  table  No. 
1  (using  averages,  but  remembering  that  results 
would  be  similar  for  individuals)  show  that  work 
delivered  in  **  ordinary  memory  '''  was  786.73 
units  (75.07  X  10.48) ;  in  ''  hurried  memory  " 
909.00  units  (94.10  X  9.66) ;  and  in  ''  best  mem- 
ory "  654.76  (60.07  X  10.90).  "  Under  the  three 
different  sets  of  conditions  three  different 
amounts  of  work  were  delivered.  This  is  exactly 
what  should  be  expected  because  of  the  varying 
conditions  under  which  the  work  was  done.  No 
one  as  yet  can  point  with  certainty  to  the  proved 


38  EXACT  MEASUREMENTS 

reasons  for  the  actual  relations  between  the  dif- 
ferent products,  but  it  is  easy  to  advance  entirely 
reasonable  explanations.  Worry,  perhaps,  or  a 
habitual  slowness  where  best  writing  is  attempted, 
would  account  for  the  small  amount  of  work 
delivered  in  *^  best  memory."  It  is  difficult  and 
nerve  trying  to  attempt  to  make  one's  hand- 
writing better  than  it  usually  is.  The  attempt 
cuts  down  the  space  and  does  not  largely  increase 
the  control.  The  loss  in  work  delivered  is  there- 
fore great.  On  the  other  hand,  it  is  usually  not 
nearly  so  difficult  or  disconcerting  to  increase 
speed  beyond  one's  average.  The  attempt  to  do 
best  work  is  a  cause  not  only  of  very  slow  prog- 
ress while  letters  and  words  are  being  written, 
but  also  of  much  loss  between  the  separate  letters 
or  words.  The  attempt  to  do  fast  writing  is  the 
cause  of  a  great  gain  in  space  (not  much  waste 
between  letters  or  words),  and  while  the  loss  in 
quality  (control)  is  considerable,  it  is  still  not 
sufficient  to  overcome  the  gain  in  space,  and  the 
work  is  correspondingly  greater.  Where  quality 
is  required  speed  drops  1/5  from  ordinary,  and 
where  speed  is  required,  quality  drops  less  than 
1/8    (see   table    No.    1  —  memory   tests).      This 


IN  EDUCATION  39 

seems  to  mean  that  there  is  less  total  loss  in 
hurried  work  than  in  best  work,  and  would  corre- 
spond with  the  results  one  would  naturally  expect 
from  the  fact  that  school  children  are  in  the 
habit  of  doing  much  hurried  writing  at  certain 
times,  while  they  have  certainly  less  habit  of 
doing  best  work  and  consequently  the  loss  is 
greater  when  best  work  is  insisted  upon. 

The  facts  just  brought  out  tend  to  justify  the 
third  claim  for  the  hypothesis  of  work;  viz.,  that 
it  settles  the  question  of  a  net  index  of  efficiency 
and  opens  the  way  toward  a  study  of  waste  in 
Education.  Using  efficiency  as  it  is  used  in 
Mechanics,  it  is  the  ratio  of  work  delivered  to 
work  done.  This  ratio  expressed  as  a  fraction 
is  the .  net  index  of  efficiency.  It  is  not  now 
known  how  to  determine  work  actually  done.  In 
handwriting,  for  example,  it  is  known  only  how 
to  determine  work  delivered  and  this  requires 
the  use  of  the  plan  suggested  in  this  paper. 
There  are  few,  however,  who  would  doubt  that 
work  done  can  eventually  be  measured,  and  when 
it  is  measured,  the  net  efficiency  index  will  be 
assured,  and  the  way  will  be  opened  for  attack 
upon  the  problem  of  waste. 


40 :  EXACT  MEASUREMENTS 

Returning,  however,  to  the  consideration  of 
work  delivered  in  handwriting,  it  is  apparent 
that  the  validity  of  the  results  depends  upon  the 
validity  of  the  Thorndike  scale,  and  upon  the 
reliability  of  judgments  of  handwriting,  which 
judgments  are  based  upon  the  scale.  Just  as  no 
additional  accuracy  is  secured  by  carrying  to 
three  decimal  places  results  based  upon  data 
carried  to  two  decimal  places  only,  so  the 
accuracy  of  computations  based  upon  imperfect 
scales  is  really  no  greater  than  the  accuracy  of 
the  scales  themselves,  and  of  the  judgments  based 
upon  the  scales.  At  present  both  of  these  items 
(the  accuracy  of  the  scale  and  the  accuracy  of 
the  judgment  based  upon  the  scale)  may  be  ques- 
tioned, and  corresponding  allowance  must  be 
made  in  placing  any  dependence  upon  computa- 
tions involving  units  derived  from  the  scales. 
Yet,  even  with  the  necessary  allowance,  valuable 
use  of  the  units  may  be  made.  Also,  the  rough- 
ness of  the  scales,  and  of  judgments  based  upon 
them,  can  be  overcome,  for  handwriting  as  a 
product  can  be  scaled  accurately  as  to  excellence. 
But  in  order  to  do  this,  a  sufficiently  large 
number    of    representative    specimens    must   be 


m  EDUCATION  41 

I  available.  One  of  the  main  objections  to  the 
I  Thorndike  scale  made  by  writing  supervisors  is 
that  the  specimens  used  were  not  representative 
of  public  school  writing  —  that  the  specimens 
were  all  largely  poor,  or  at  least  indifferent,  and 
that  the  really  good  qualities  were  not  fairly 
represented.  However  this  may  be,  it  at  least 
raises  the  question  of  what  grade  of  handwriting 
may  properly  be  expected  of  public  school  chil- 
dren, and  how  is  the  quality  of  handwriting  to 
be  judged,  anyhow?  Did  Thorndike  have  repre- 
sentative specimens  and  how  is  one  to  tell  what 
is  representative?  The  judgment  of  quality  and 
therefore  of  the  scale,  must  be  based  upon  the 
opinion  of  some  one  as  to  what  is  or  is  not  excel- 
lent. No  machine  can  ever  set  up  standards  of 
excellence.  No  machine  can  ever  decide  as  to 
whether  a  vertical  or  a  slant  penmanship  is  bet- 
ter, or  as  to  whether  legibility  is  worth  more 
than  beauty  etc.,  etc. ;  but  agreement  can  be  made 
upon  these  points,  and  when  this  has  been  done, 
it  is  conceivable  that  a  machine  could  be  made 
to  tell  whether  or  not  a  given  specimen  is  up 
to  the  standard.  Neither  is  it  imperative  that 
large  numbers  of  persons  should  be  employed  in 


42  EXACT  MEASUREMENTS 

the  setting  up  of  the  standards,  except  in  the 
sense  that  large  numbers  must  agree  to  the  stand- 
ard as  set  up.  That  is  to  say,  in  this  case 
as  elsewhere,  all  could  defer  to  a  single  authority, 
and  agree  to  accept  the  grading  of  one  expert, 
and  to  use  his  scale.  It  is  better,  probably,  to 
get  the  judgment  of  many  experts,  as  Thorndike 
did,  and  to  agree  to  abide  by  the  collective  judg- 
ment. But  the  fundamental  thing  is  the  agree- 
ment, just  as  in  any  discussion  there  must  be  an 
agreement  upon  a  definition  of  terms,  after  which 
it  is  possible  for  the  persons  to  understand  each 
other  and  to  talk  definitely  in  the  terms  of  the 
agreement. 

Whether  or  not  the  Thorndike  scale  is  the  best 
upon  which  to  agree,  the  future  will  tell.  So 
far  as  the  report  shows,  only  a  very  general  basis 
of  judgment  was  proposed  to  the  judges,  and  it 
is  probable  that  before  there  can  be  a  final  scale 
a  more  definite  agreement  must  be  reached  as 
to  what  constitutes  excellence  in  handwriting.  Is 
it  beauty,  neatness,  size,  slant,  or  legibility  (mere 
legibility  as  was  assumed  in  the  making  of  the 
Ayres  scale)  ?  There  seems  to  be  at  present  no 
general  agreement  upon  these  points ;  but  never- 


IN  EDUCATION  43 

theless  the  scales  can  be  used  profitably,  and  an 
understanding  maintained  in  their  use  as  long 
as  it  is  known  what  they  actually  represent,  no 
matter  whether  or  not  there  is  a  final  agreement 
as  to  what  they  might  represent.  If  the  terms 
are  defined,  the  discussion  can  proceed  on  the 
basis  of  the  definition,  and  the  only  further 
progress  consists  in  the  elaboration  of  a  defini- 
tion which  all  can  more  fully  accept.  But 
granted  the  definition;  i.  e.  the  scale,  a  mechan- 
ical method  of  judging  a  certain  specimen  by  the 
scale  may  be  looked  forward  to.  In  the  analysis 
of  handwriting  for  the  detection  of  forgeries 
such  a  method  as  been  worked  out.  Enough  of 
mechanical  analysis  is  made  so  that  the  real 
essence  of  the  particular  writing  is  plainly  seen. 
Looking  to  other  fields  it  is  recalled  that  a 
mechanical  analysis  of  a  play  decides  how  much 
of  it  Shakespeare  really  wrote.  In  a  similar  way 
the  authorship  of  a  picture  may  be  determined. 
It  is  in  this  direction  that  the  movement  will  be 
made  to  remove  the  personal  factor  in  scoring 
by  such  scales  as  the  Thorndike  scale  in  hand- 
writing. In  the  meantime  Education  is  far  better 
off  with  the  imperfect  scales  which  it  has  (even 


44  EXACT  MEASUREMENTS 

with  imperfect  use  of  them)  than  it  was  before 
it  had  them;  but  this  advantage  can  be  immeas- 
urably increased  if  these  scales  are  at  once  made 
to  yield  real  units  of  work  and  rate-of-work 
(power). 

With  this  outlook,  there  must  be  scales  and 
units  in  other  subjects  than  penmanship,  and 
other  units  of  work  and  rate-of-work  (power). 
This  means  many  scales  and  many  units  in  many 
specific  subjects.  Some  of  these  scales  are 
already  extant  and  the  work  in  making  others 
will  be  worth  all  that  it  costs,  for  when  they  are 
made  and  gradually  refined,  and  when  from  them 
real  units  of  work  and  rate-of-work  (power)  have 
been  made,  and  used  as  a  basis  for  comparison 
of  individuals  and  of  schools,  the  progress 
involved  will  be  very  great. 


IN  EDUCATION 


n 

But  the  solution  of  the  problem  of  school  meas- 
urement should  not  be  limited  to  the  computation 
of  many  kinds  of  work,  by  many  standards,  in 
many  school  subjects.  There  is  a  need  for  a 
single  measure,  covering  all  subjects,  which  shall 
give  a  sort  of  summary  of  the  abilities  of  an 
individual  or  of  a  group.  This  has  been  gen- 
erally and  correctly  expressed  as  a  need  for  a 
measure  of  intelligence  itself ;  but  it  is  also  more 
than  that.  It  is  a  need  for  the  computation  of 
that  which,  for  want  of  a  better  name,  may  be 
called  mental  work.  As  already  stated  in  another 
part  of  the  paper,  purely  mental  work  cannot  be 
computed  so  long  as  the  force  involved  is  partly 
intelligent  and  partly  mechanical,  as  it  is  in  hand- 
writing. But  mental  work  can  be  computed  by 
the  plan  already  outlined  for  penmanship  work, 
if  intelligence  is  a  force,  and  if  it  can  be  dealt 
with  apart  from  any  mechanical  factors.  It  is 
believed  that  this  can  be  done. 

Intelligence  is  a  force,  which  by  acting  through 


46  EXACT  MEASUREMENTS 

a  certain  space,  does  work.  Intelligence  should 
not  be  regarded  as  merely  analogous  to  force. 
It  should  be  identified  with  force,  since  it  meets 
the  requirements  of  the  definition  of  force.  It 
is  that  which  changes  (controls)  the  motion  of 
bodies;  it  is  that  ^'  which  makes  it  happen." 
Just  as  much  is  known  about  it  (and  no  more), 
as  is  known  about  other  forces.  It  would  not  be 
known  to  exist  were  it  not  seen  revealing  itself 
in  action.  A  way  is  later  suggested  for  freeing 
it  from  mechanical  factors. 

But  as  already  suggested,  the  need  is  not  met 
by  the  use  of  a  scale  of  intelligence  (force)  alone. 
The  main  use  for  such  a  scale  is  for  purposes  of 
comparison,  and  for  such  purposes  there  must  be 
considered,  also,  the  space  through  which  a  given 
measure  of  the  force  acts  in  a  given  time.  To 
forget  this  is  to  violate  the  same  principle  which 
is  violated  when  the  penmanship  of  schools  is 
compared  by  stating  control  (quantity  of  quality) 
alone,  without  asking  through  how  much  space 
(number  of  letters)  the  control  acts  in  a  given 
time.  So  while  intelligence  is  to  be  dealt  with 
as  a  force,  it  must  also  be  dealt  with  as  acting 
through  space.     But  does  it  act  through  space? 


IN  EDUCATION  47 

It  is  certain  that  in  so  far  as  the  presence  of 
intelligence  can  be  proved,  the  proof  results  from 
the  observation  of  some  kind  of  expression  or 
action  through  which  intelligence  reveals  itself. 
Action  takes  place  in  space,  and  the  space  may 
always  be  measured  in  the  elements  of  the  action. 
In  handwriting  the  elements  used  were  letters. 
In  the  broader  attempt  to  measure  the  space 
through  which  intelligence  acts,  the  expression 
is  found  to  be  not  only  in  written  words  (or  let- 
ters), but  also  in  vocal  sounds  or  in  gestures 
which  involve  the  body  in  whole  or  in  part. 
While  these  different  types  of  expression  present 
many  difficulties  when  the  attempt  is  made  to 
count  their  elements  as  a  measure  of  space,  yet 
the  difficulties  do  not  seem  insurmountable,  at 
least  for  the  purpose  of  a  rough  scale. 

The  problem,  therefore,  which  is  clearly  in 
view,  is  that  of  regarding  intelligence  as  a  force 
acting  through  space,  of  scaling  the  force  and 
of  scaling  the  space,  and  of  combining  the  stand- 
ard units  of  these  two  scales  into  a  stand- 
ard unit  of  mental  work  (thereby  also  making 
possible  a  unit  of  rate-of-work)  (power).  A  ten- 
tative method  of  scaling  the  space  has  already 


48  EXACT  MEASUREMENTS 

been  suggested;  but  what  can  be  done  with 
regard  to  a  scale  of  the  force,  intelligence?  It 
has  already  been  said  that  we  do  not  know  what 
intelligence  is,  but  its  existence  is  proved  just  in 
the  same  way  that  the  existence  of  other  forces  is 
proved ;  viz.,  by  its  effects.  It  is  not  known  what 
gravitation  is,  but  the  falling  of  unsupported 
bodies  is  accepted  as  evidence  of  gravitation.  A 
study  of  the  literature  of  psychology  will  show 
that  in  like  manner,  adjustment  to  environment  is 
generally  accepted  as  an  indication  of  intelligence. 
Intelligence  is  here  conceived  as  the  indefinable 
subjective  force  which,  through  all  degrees  of 
consciousness  and  intention,  ^^  makes  it  happen." 
But  from  this  point  of  view  mere  adjustment 
cannot  be  taken  as  definite  proof  of  intelligence, 
for  there  are  recognized  certain  unintelligent 
adjustments,  and  certain  others  which  may  or 
may  not  be  intelligent.  The  tropisms  of  Loeb 
and  the  '^  pure  instincts  "  of  other  writers  are 
unintelligent  because  they  are  described  as  utiliz- 
ing a  sort  of  hair-trigger  mechanism  which  re- 
quires for  its  release  no  impulse  of  any  kind 
from  within,  but  merely  the  appropriate  external 
stimulus.     Other  reactions  which  once  required 


IN  EDUCATION  49 

intelligence,  may  through  use,  come  to  be  per- 
formed sometimes  with  and  sometimes  (rela- 
tively at  least)  without  that  factor,  and  there  is 
no  way  for  the  observer  to  make  a  distinction. 
In  the  case  of  the  responses  gained  by  use,  it 
can  be  known  that  a  past  intelligence  has  been 
exercised,  but  not  proved  that  a  current,  imme- 
diate intelligence  is  being  exercised.  Current, 
immediate  intelligence  can  be  proved  in  one  way 
only.  The  proof  lies  not  in  the  tropisms  which 
give  an  invariable  response  to  fixed  conditions, 
nor  yet  in  the  reactions  which  have  become 
mechanized  to  a  greater  or  lesser  degree,  and  so 
may  or  may  not  be  at  the  moment  intelligently 
directed;  but  it  lies  in  consistent  and  effective 
reaction  to  variable  conditions  —  to  conditions 
tvMch  are  novel  at  the  time  at  which  the  reaction 
occurs.  Such  reactions  introduce  a  factor  of 
selection,  and  where  this  factor  is  observed  a 
subjective  control,  intelligence,  is  inferred. 

Hence  if  intelligence  is  to  be  graded  it  seems 
logical  to  make  the  grading  in  terms  of  this  same 
principle  of  effective  reaction  to  novel  conditions. 
This  can  be  done,  for  there  are  already  recog- 
nized a  number  of  very  distinct  ways  by  which 


50  EXACT  MEASUREMENTS 

living  creatures  respond  to  novel  conditions  with 
varying  degrees  of  success.  One  list  quite  com- 
monly accepted  contains  (1)  trial  and  error,  (2) 
imitation,  (3)  *'  free  ideas."  Some  psychologists 
prefer  to  alter  this  list,  using  in  the  lower  stages 
other  terms,  such  as  tropism,  instinct,  or  circu- 
lar process,  and  discriminating  in  the  ^*  free 
idea  "  stage  distinct  divisions,  such  as  sugges- 
tion, dictation,  association,  and  thought.  There 
is  probably  no  universally  accepted  list ;  but  since 
some  definite  list  could  certainly  be  agreed  upon 
when  the  need  for  such  agreement  becomes  evi- 
dent^ any  list  may  be  taken  for  purposes  of  illus- 
tration. If  such  a  list  included  (for  example) 
(1)  trial  and  error,  (2)  imitation,  (3)  suggestion, 
(4)  association,  (5)  thought,  then  these  would  be 
the  five  grades  in  a  scale  of  intelligence. 

But  these  grades  must  not  be  known,  merely. 
They  must  be  known  in  series,  one  higher  in  a 
scale  than  is  another.  And  not  only  that,  but  the 
numerical  relation  between  the  grades  must  be 
known  in  order  that  any  one  of  them  may  be 
expressed  in  terms  of  any  other.  In  a  general 
way  it  is  accepted  that  imitation  is  higher  (in  a 
scale  of  intelligence)  than  is  trial  and  error,  and 


IN  EDUCATION  51 

thought  higher  than  either  imitation  or  trial  and 
error.  That  creature  which  can  respond  by  trial 
and  error  only,  would  probably  be  least  success- 
ful in  meeting  novel  conditions,  and  therefore 
called  least  intelligent.  That  creature  which 
could  respond  by  imitation  or  by  thought,  would 
be  more  successful  and  would  therefore  be  said 
to  possess  a  higher  grade  of  intelligence.  But  in 
relation  to  the  principle  of  response  to  novel  con- 
ditions, the  order  in  which  these  types  of 
response  stand  can  be  definitely  determined ;  and 
not  only  the  order,  but  also  the  mathematical 
relation  between  them.  Through  reasonable  pa- 
tience in  experimentation,  the  average  percentage 
of  success  (per  thousand  or  other  large  number 
of  cases),  occurring  for  each  one  of  the  types  can 
be  determined.  The  relation  between  successive 
percentages  will  be  the  relation  between  the  steps 
of  the  scale.  Tropism  or  some  other  method 
agreed  upon  as  one  which  brings  no  success  will 
be  the  zero. 

Preliminary  work  on  such  a  scale  is  now  being 
done  by  the  writer,  and  if  the  results  are  suffi- 
ciently promising  they  will  later  be  offered  for 
criticism,    and   the   aid    of   educational    experts 


52  EXACT  MEASUREMENTS 

sought  in  their  revision.  When  there  is  such  a 
scale  of  force  and  also  a  scale  of  space  (which 
is  likewise  being  worked  upon),  unit  force  and 
unit  space  can  be  combined  into  a  composite 
quantity-quality  unit  of  mental  work.  When  this 
unit  is  complicated  with  unit  time  it  will  furnish 
a  unit  of  rate-of -mental-work  (mental  power), 
which  unit  will  be  a  fair  one  to  use  in  compari- 
sons of  individuals,  of  schools,  or  any  other 
groups,  because  all  factors  will  have  been  con- 
sidered. In  connection  with  the  unit  there  will 
be  needed  a  series  of  tests,  by  the  use  of  which 
data  may  be  obtained  for  computations  in  terms 
of  the  units.  This  series  of  tests  (largely  similar, 
probably,  to  those  by  which  the  scale  must  be 
established)  will,  if  successful,  be  such  as  to  make 
it  possible  for  subjects  of  all  ages  to  be  tested 
for  the  various  grades  of  intelligence,  and  for 
the  space  through  which  the  intelligence  can  act 
in  a  certain  time.  From  these  data  the  number 
of  units  of  mental  work  can  be  computed.  A 
purely  arbitrary  illustration  is  as  follows : 

An  intelligence  of  grade  6.00  acts  through  a 
space  of  grade  50.00  in  one  minute.  6.00  X  50.00 
(F  X  S)  =300.00  units  of  mental  work  per  min- 


IN  EDUCATION  53 

ute.  Suppose  the  standard  (arbitrarily  placed  or 
found  by  experiment  —  see  penmanship  illustra- 
tion) to  be  275.00  units  per  minute.  300.00  di- 
vided by  275.00  =  1.09  units  of  rate-of-mental- 
work  (the  rating  of  this  imaginary  individual  at 
that  time). 

It  should  be  noted  here  that  an  increase  or 
decrease  in  mental  work  does  not  necessarily 
mean  an  increase  or  decrease  in  the  one  factor, 
intelligence.  The  change  may  be  in  either  of  the 
other  factors,  the  space  or  the  time.  The  weight 
of  this  fact  will  be  evident  in  what  follows  con- 
cerning the  Binet-Simon  tests  of  intelligence. 

No  such  discussion  as  this  would  be  complete 
without  a  consideration  of  the  Binet-Simon  tests 
(the  most  popular  of  all  the  tests  already  avail- 
able which  make  any  attempt  to  scale  the  force 
involved  in  a  computation  of  mental  work). 
These  tests  have  given,  and  are  continuing  to 
give,  very  valuable  service;  but  even  their  most 
enthusiastic  advocates  do  not  claim  them  to  be 
tests  of  immediate  (current)  intelligence  alone. 
Probably  the  most  that  can  be  said  is  that  they 
are  tests  of  a  combination  of  immediate  and  past 
intelligence  and  of  inherited  mechanism.     They 


.54  EXACT  MEASUREMENTS 

are  tests  of  what  a  subject  can  do,  as  a  result  of 
his  total  equipment  and  experience.  The  intel- 
ligence which  enabled  him  to  meet  novel  condi- 
tions and  to  adjust  himself  to  them,  may  or  may 
not  be  present,  for  many  of  the  tests  do  not  call 
for  a  meeting  of  novel  conditions  at  the  time  of 
the  test,  but  for  a  repetition  of  acts  the  capability 
for  doing  which  may  have  demanded  a  meeting 
of  novel  conditions  in  the  past.  This  is  one  lim- 
itation upon  the  use  of  these  tests  for  the  pur- 
pose of  obtaining  data  to  be  used  in  the  computa- 
tion of  mental  work,  for  the  computing  of  the 
mental  work  accomplished  in  any  unit  of  time 
requires  that  the  force  involved  in  the  computa- 
tion shall  be  immediate  intelligence  (adjustment 
to  novel  conditions  at  that  time). 

It  is  also  noted  that  the  steps  in  the  Binet- 
Simon  scale  are  expressed  in  years,  and  it  hardly 
seems  possible  that  the  mathematical  relation 
between  the  accomplishment  of  the  various  years 
can  ever  be  known  accurately  enough  (even  by 
the  law  of  averages).  Mental  development  does 
not  seem  readily  measurable  in  years  of  life  as  a 
standard.  It  is  at  least  unproved  (and  probably 
unclaimed)  that  the  scale  as  it  stands  presents 


IN  EDUCATION  55 

any  way  by  which  one  grade  couid  be  expressed 
in  terms  of  any  other  grade.  But  if  an  expres- 
sion in  equivalents  could  be  approximated,  and 
if  the  fact  that  immediate  intelligence  is  not  set 
squarely  by  itself  could  be  temporarily  over- 
looked, the  scale  would  then  be  useable  for  at 
least  rough  computations ;  but  even  then  it  would 
not  be  fair  to  test  subjects  and  to  use  the  data 
for  comj^arison  unless  allowance  were  made  for 
the  error  resulting  from  a  failure  to  consider  the 
space  through  which  the  force  acts  in  a  given 
time.  As  the  tests  now  stand,  this  question  is 
not  raised  except  in  a  few  specific  instances.  The 
examiner  waits  for  the  dull  child,  encourages  or 
possibly  forces  him,  as  the  case  seems  to  require, 
in  order  to  get  his  maximum  effort  without 
regard  to  time.  Then  he  is  given  a  certain 
^'  mental  age  '^  because  he  passes  a  certain  num- 
ber of  points.  If,  now,  a  bright  child  be  taken  — 
one  younger  chronologically  but  quicker  and  more 
alive  in  every  way  —  and  if,  in  half  of  the  time, 
results  are  easily  obtained  which  indicate  the 
same  mental  age,  this  procedure  does  not  show 
that  the  two  children  belong  together.  Children 
belong  together  who  are  equal  or  approximately 


56  EXACT  MEASUREMENTS 

equal  in  ability  to  do  mental  ivork.  The  real  test 
must  regard  the  space,  and  the  time,  and  the 
force,  and  make  work  and  rate-of-work  (power) 
the  basis  for  comparison.  Then  it  will  be  found 
that  two  children  such  as  those  cited  are  far 
apart.  It  is  found  that  children  tested  by  the 
Binet-Simon  tests,  assigned  the  same  mental  age 
(below  chronological  age)  and  put  in  classes  of 
normal  children  of  the  given  mental  age,  are 
unable  to  do  the  work.  Also,  children  found  to 
be  below  normal  age  and  segregated  in  special 
classes  of  supposed  approximate  ages  are  found 
not  to  work  well  together  after  a  time.  They 
are  like  swimmers  who  go  at  various  rates  and 
who  constantly  draw  away  from  each  other. 
These  are  the  natural  conditions  which  should 
be  expected  under  a  system  of  partial  testing. 
The  recognition  of  the  fact  that  they  work  out 
as  they  do,  throws  weight  in  favor  of  the  conten- 
tion that  time,  force,  and  space  should  all  be  con- 
sidered, and  that  the  computation  of  work  smd 
rate-of-worh  (power)  is  the  ultimate  goal  of 
school  measurement. 

[In  this  paper  the  units  used  have  been  pat- 
terned upon  what  the  physicist  calls  his  arbitrary 


IN  EDUCATION  57 

units,  sucli  as  those  based  upon  gravitation.  The 
physicist  also  uses  other  units  called  ^*  absolute  " 
units,  such  as  those  based  upon  acceleration. 
Some  of  the  phenomena  of  mental  activity;  e.  g. 
the  ^^  warming  up  "  process,  Weber's  law,  and 
the  fact  that  one  probably  accomplishes  more  per 
minute  in  the  last  minutes  of  a  test  than  in  the 
first  —  at  least  raise  the  question  as  to  whether 
absolute  units,  based  upon  acceleration  may  not 
in  the  future  find  a  place  in  the  computation  of 
mental  work.] 


Credit  is  due  to  J.  S.  Gaylord,  Phychology,  Winona 
Normal  School,  and  to  W.  H.  Munson,  Physics,  Winona 
Normal  School,  for  definite  constructive  criticism  of  this 
paper. 


Country  Life  and  the  Country  School 

Mabel  Carney,  408  pp $1.25 

The  book  gives  a  true  portrayal  of  existing  rural  conditions ; 
presents  a  definite,  constructive  program  for  improvement ;  and 
strikes  a  clear  note  of  inspiration  for  organized  endeavor. 

Principles  of  Teaching 

N.  A.  Harvey,  423  pp $1.25 

The  aim  has  been  to  make  a  thoroughly  practical  book  for 
all  teachers.  Almost  every  difficult  problem  the  teacher  has  to 
face  is  discussed  in  an  interesting,  helpful  way.  Especially  val- 
uable are  the  chapters  on  the  Definition  of  Education,  Theory 
of  Play,  Interest,  Analysis  of  the  Study  Process,  and  Motives 
in  School. 

Methods  of  Teaching 

W.  W.  Charters,  444  pp $1.25 

Among  the  first  to  try  to  work  out  general  methods  of  teach- 
ing in  terms  of  the  function  of  subject  matter.  Dr.  Charters 
has  been  more  consistent  and  has  elaborated  the  point  of  view 
more  fully  and  more  clearly  than  any  other  writer.  It  is  a 
most  stimulating  and  informing  book,  especially  designed  for 
use  as  a  text  in  Normal  and  Training  schools. 

The  Personality  of  the  Teacher 

Charles  McKenny,   192  pp $1.00 

It  is  generally  conceded  that  the  prime  factor  in  making  a 
school  is  the  personality  of  the  teacher.  The  author  shows 
what  qualities  go  to  make  up  that  desirable  personality  and 
how  to  develop  those  qualities.  The  book  cannot  fail  to  prove 
a  source  of  inspiration  and  strength. 

How  to  Teach  Arithmetic 

J.  C.  Brown  and  L.  D.  Coffman,  384  pp $1.25 ^ 

The  aim  has  been  to  present  in  a  clear  and  definite  way  the 
principles  and  devices  with  which  efficient  teachers  of  Arith- 
metic should  be  familiar. 

The  selection  and  arrangement  of  the  material  shows  sound 
pedagogical  principles;  there  is  an  abundance  of  illustrative 
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ROW,  PETERSON  &  COMPANY 
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The  Educational  Meaning  of  Manual 
Arts  and  Industries 

By  R.  K.  ROW 

Cloth,  250  pages  Price,  $1.25 

The  aim  of  the  author  is  to  present  an  or- 
ganized view  of  the  whole  problem  of  the  signifi- 
cance of  manual  arts  and  industries  in  a  system  of 
education.     To  this  end  he  — 

First:  Defines  the  problem  of  the  book. 

Second  :  Throws  into  perspective  the  history  of  the  develop* 
ment  of  manual  training  as  a  factor  in  education. 

Third:  Analyzes  and  explains  the  primary  impulses  and 
interests  in  manual  activities. 

Fourth:  Shows  the  relation  of  manual  activities  to  sense 
training,  motor  control  and  neuro-muscular  development. 

Fifth:  Discusses  the  intellectual,  aesthetic,  ethical,  eco- 
nomic, and  social  values  of  training  in  manual  arts  and 
industries. 

Sixth:  Shows  to  whom  such  training  is  of  most  value,  out- 
lines a  general  method  of  teaching,  and  gives  suggestions 
for  a  course  of  study. 

SOME    ESTIMATES 

The  most  complete  and  intelligent  tliesis  thus  far  published  on  the 
value  of  manual  training  in  the  schools. — Chicago  Record-Herald, 

Mr.  Row  never  forgets  the  claims  of  education  in  vocation.  His  study 
has  been  careful  and  scholastic,  his  treatment  professional  and  patriotic, 
his  methods  are  pedagogical,  and  his  style  is  attractive. — New  England 
Journal  of  Education, 

Mr.  Row's  discussion  of  intellectual,  aesthetic,  ethical,  economic,  and 
social  values  is  especially  attractive  and  strong. — Moderator-Topics, 

The  large  view  th^t  the  author  takes  of  manual  training  and  its  wide 
application  gives  his  book  place  as  an  effort  that  has  not  been  anticipated 
by  any  other  in  its  field. — Chrisiim  Science  Monitor^ 

Sent  postpaid  on  receipt  of  price. 

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SCHOOL  MANAGEMENT 

By  ALBERT  SALISBURY,  Ph.  D. 

President  of  the  Whitewater  State  Normal  School,  author  ol 
"The  Theory  of  Teaching,"  etc. 

Cloth.  12mo..  196  pages,  $1.00 

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and  in  the  training  of  teachers.  School  conditions  have  changed 
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excellent  a  few  years  ago  are  now  antiquated.  Much  more  is 
demanded  of  the  teacher  than  formerly.  He  has,  in  fact,  become 
an  official  of  the  state,  w^ith  larger  functions  and  a  greater  need 
for  intelligence  concerning  those  functions  than  the  old-time 
pedagog. 

While  endeavoring  to  recognize  this  newer  conception  of  the 
teacher's  office,  and  the  greater  burden  which  it  imposes,  it  has 
been  the  desire  of  the  author  to  make  a  small  book  rather  than  a 
bulky  one,  excluding  padding  and  time-honored  common-place. 
The  book  is  intended  to  serve  the  needs  of  young  teachers  and 
those  in  preparation  for  the  work,  and  clearness  has  been  aimed 
at  rather  than  profundity. 

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it  includes.  It  is  ri^ht  in  size,  covers  the  necessary  ground,  and  occupies  safe 
and  sane  positions.  ' 

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"A  long  life  in  the  schoolroom  as  a  trainer  of  teachers  and  a  man  who  has 
kept  pace  w^ith  educational  progress.  President  Salisbury  has  written  a  practical 
book  with  little  theory  and  every  paragraph  driving  home  principles  for  the  safe 
guidance  of  teachers.  His  vigorous  style,  his  coming-to-the-point-quick  man- 
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